A Chicken and a Half?!Date: 05/07/97 at 09:54:56 From: Steve Green Subject: Word problem Dad asks all the time If a chicken and a half lays an egg and a half in a day and a half, how long does it take to get a dozen eggs? Date: 05/13/97 at 10:58:32 From: Doctor Sonya Subject: Re: Word problem Dad asks all the time Dear Steve, This question feels strange to answer, because dealing with half chickens and half eggs is not something one normally encounters. Because I have no intuitive understanding of half a chicken, I'll approach this problem by plugging in simple numbers for the complicated numbers (like one and a half). Let's say we have 1 chicken that lays 1 egg in 1 day. Then how many days would it take to get a dozen eggs? 12, right? Now if we have 2 chickens that lay 2 eggs in, say, 3 days, how long does it take to get a dozen eggs? Since we are getting 4 eggs every 3 days out of these two chickens, it will take 3*3 = 9 days. So what exactly are we doing when we solve these chicken-egg problems? Let's see. What I am doing is seeing how many eggs are laid total per cycle. In the second situation above, each cycle is three days long. Then I find out how many cycles we'll need to go through to get 12 eggs. If we get 4 eggs per cycle, we'll need 12/4 = 3 cycles. Now I multiply the number of cycles by the length of each cycle to get the total time it will take. This gives me 3*3 = 9 days. So 2 chickens who each lay 2 eggs in three days take 9 days to lay a dozen eggs. This method should work no matter what our numbers are. Try plugging in the chicken and a half, the egg and a half, and the day and a half, and see what you get. Write us back if you need more help. -Doctor Sonya, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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